There are so many stabilizers for you to choose from that it makes it hard to select the right one for the job. Below are a few links to education sites and documents about keeping things stable.
My favorite stabilizers are the following:
These can be purchased from many different companies.
Cut Away - White for sweatshirts
Cut Away Black for dark fabrics
No Show Fusible Mesh - this is great for t-shirts and quilting blocks
Tear Away Wash Away - another stabilizer good for quilting
Clear Wash Away - towels and anything needing a topper
Aqua Wash Away - the best for lace
Click to link to Embroidery Library's Guide Page
Click to link to Sewing & Craft Club Stabilizer Guide Page
Click to link to Sulky's Stabilizer Guide Page
Click to download Hollingsworths Educational Page
Threads Magazine shares stabilizers information by clicking this link
Click to download Babylock's Education page for stabilizers
Check your download folder for the files that automatically are downloaded to your computer.